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1: Bibliography

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SPHEREPACK 2.0: A Model Development Facility. NCAR Technical Note Technical Report TN-436-STR, National Center for Atmospheric Research.

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Notes:

SPHEREPACK 2.0 is a collection of Fortran programs that facilitates computer modeling of geophysical processes. Accurate solutions are obtained via the spectral method that uses both scalar and vector spherical harmonic transforms. The package also contains utility programs for computing the associated Legendre functions. SPHEREPACK 3.1 was released in August 2003.

External Links:

FullText, SPHEREPACK 3.1

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1st item.

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The $J$-Matrix Method. Developments and Applications. Springer-Verlag.

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ISBN 978-1-4020-6072-4

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§18.39(iv).

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Pfaff’s method II: Diverse applications. J. Comput. Appl. Math. 68 (1-2), pp. 15–23.

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ISSN 0377-0427, Document, MathReview (Bruce C. Berndt), ZentralBlatt

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§17.7(iii).

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On magic squares constructed by the uniform step method. Proc. Amer. Math. Soc. 2 (4), pp. 557–565.

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ISSN 0002-9939, Fulltext, MathReview (D. H. Lehmer), ZentralBlatt

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§27.17.

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Mathematical Methods for Physicists. 6th edition, Elsevier, Oxford.

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ISBN 0-12-059876-0;0-12-088584-0, MathReview, ZentralBlatt

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§1.17(ii), §1.17(iii).

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2: Bibliography M

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Rational approximations, software and test methods for sine and cosine integrals. Numer. Algorithms 12 (3-4), pp. 259–272.

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Notes:

Includes Fortran code, maximum accuracy 20S.

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ISSN 1017-1398, Document, MathReview, ZentralBlatt

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§6.13, 4th item, §6.21(ii).

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Geometrical and Catastrophe Optics Methods in Scattering. In Physical Acoustics, A. D. Pierce and R. N. Thurston (Eds.), Vol. 21, pp. 1–234.

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§36.14(ii).

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Numerical Methods for Roots of Polynomials. Part I. Studies in Computational Mathematics, Vol. 14, Elsevier, Amsterdam.

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ISBN 978-0-444-52729-5; 0-444-52729-X, MathReview Entry, ZentralBlatt

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§3.8(iv).

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Spectral functions for the Tomonaga-Luttinger model. Phys. Rev. B 46 (24), pp. 15753–15760.

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Document

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§13.28(iii).

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Methods and Programs for Mathematical Functions. Ellis Horwood Ltd., Chichester.

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Notes:

Includes diskette

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ISBN 0-13-578998-2, MathReview, ZentralBlatt

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2nd item, CEPHES (free C library).

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3: Bibliography K

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Numerical Methods and Software. Prentice Hall, Englewood Cliffs, N.J..

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Notes:

Includes collection of single- and double-precision Fortran subroutines.

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ISBN 0-13-627258-4, GAMS (package NMS), ZentralBlatt

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NMS (free collection of Fortran subroutines).

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Periodic Orbits, Spectral Statistics, and the Riemann Zeros. In Supersymmetry and Trace Formulae: Chaos and Disorder, J. P. Keating, D. E. Khmelnitskii, and I. V. Lerner (Eds.), pp. 1–15.

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§25.17.

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Methods of computing the Riemann zeta-function and some generalizations of it. USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.

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Document, MathReview (Matti Jutila), ZentralBlatt

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§25.18(i).

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The Rayleigh function: Theory and computational methods. Zh. Vychisl. Mat. Mat. Fiz. 39 (12), pp. 1962–2006.

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Translation in Comput. Math. Math. Phys. 39 (1999), No. 12, pp. 1883–1925.

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ISSN 0044-4669, MathReview (Walter Gautschi), ZentralBlatt

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§10.21(xiii).

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An indirect method for evaluating certain infinite integrals. Z. Angew. Math. Phys. 29 (3), pp. 380–386.

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ISSN 0044-2275, Document, MathReview, ZentralBlatt

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§10.71(ii).

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4: 18.39 Applications in the Physical Sciences

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§18.39(iii) Non Classical Weight Functions of Utility in DVR Method in the Physical Sciences

►Shizgal (2015) gives a broad overview of techniques and applications of spectral and pseudo-spectral methods to problems arising in theoretical chemistry, chemical kinetics, transport theory, and astrophysics. … ►Shizgal (2015, Chapter 2), contains a broad-ranged discussion of methods and applications for these, and other, non-classical weight functions. … ►

§18.39(iv) Coulomb–Pollaczek Polynomials and J-Matrix Methods

… ►The technique to accomplish this follows the DVR idea, in which methods are based on finding tridiagonal representations of the co-ordinate, $x$. …

5: Bibliography G

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WKB and turning point theory for second-order difference equations. In Spectral Methods for Operators of Mathematical Physics, Oper. Theory Adv. Appl., Vol. 154, pp. 101–138.

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External Links:

FullText, MathReview (Ioannis K. Purnaras), ZentralBlatt

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§18.15(v), §18.15(v).

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Algorithm 939: computation of the Marcum Q-function. ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.

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Notes:

Includes Fortran program claiming 12S accuracy

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ISSN 0098-3500, Link, Document, MathReview Entry, ZentralBlatt

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3rd item, §10.77(ix).

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A method for evaluating certain Bessel integrals. Z. Angew. Math. Phys. 30 (4), pp. 722–723.

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ISSN 0044-2275, Document, MathReview

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§10.71(ii).

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Numerical Analysis of Spectral Methods: Theory and Applications. Society for Industrial and Applied Mathematics, Philadelphia, PA.

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Notes:

CBMS-NSF Regional Conference Series in Applied Mathematics, No. 26

External Links:

MathReview (O. Widlund), ZentralBlatt

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§18.38(i).

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Spectral Methods and Their Applications. World Scientific Publishing Co. Inc., River Edge, NJ-Singapore.

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ISBN 981-02-3333-7, MathReview (K. Moszyński), ZentralBlatt

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§18.38(i).

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6: Bibliography D

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Methods of Numerical Integration. 2nd edition, Computer Science and Applied Mathematics, Academic Press Inc., Orlando, FL.

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ISBN 0-12-206360-0, MathReview (John P. Coleman), ZentralBlatt

Referenced by:

§3.5(iii), §3.5(i), §3.5(i), §3.5(ii), §3.5(iii), §3.5(iv), §3.5(v), §3.5(vi), §3.5(vii), §3.5(x).

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Asymptotic Methods in Analysis. 2nd edition, Bibliotheca Mathematica, Vol. IV, North-Holland Publishing Co., Amsterdam.

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MathReview, ZentralBlatt

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§2.2, Ch.2, §26.7(iv), §26.7(iv), §4.13.

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Unification of one-dimensional Fokker-Planck equations beyond hypergeometrics: Factorizer solution method and eigenvalue schemes. Phys. Rev. E (3) 57 (1), pp. 252–275.

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ISSN 1063-651X, Document, MathReview (Victor I. Stepanov), ZentralBlatt

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§31.17(ii).

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Computing spectra of linear operators using the Floquet-Fourier-Hill method. J. Comput. Phys. 219 (1), pp. 296–321.

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ISSN 0021-9991, MathReview, ZentralBlatt

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§22.11.

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Linear operators. Part II. Wiley Classics Library, John Wiley & Sons, Inc., New York.

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Spectral theory. Selfadjoint operators in Hilbert space, With the assistance of William G. Bade and Robert G. Bartle, Reprint of the 1963 original, A Wiley-Interscience Publication

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ISBN 0-471-60847-5, MathReview Entry

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(1.18.68), §1.18(ix), §1.18(ix), §1.18(ix), §1.18(x).

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7: Bibliography R

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Methods of Modern Mathematical Physics, Vol. 2, Fourier Analysis, Self-Adjointness. Academic Press, New York.

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ISBN 978-0-12-585002-5, MathReview Entry

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§1.18(x).

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Methods of Modern Mathematical Physics, Vol. 4, Analysis of Operators. Academic Press, New York.

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ISBN 0-12-585004-2(vol.4), MathReview (P. R. Chernoff)

Referenced by:

§1.18(x).

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Methods of Modern Mathematical Physics, Vol. 3, Scattering Theory. Academic Press, New York.

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External Links:

ISBN 0-12-585003-4 (vol.3), MathReview (P. R. Chernoff)

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§1.18(x).

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Erratum to:Relationships between the zeros, weights, and weight functions of orthogonal polynomials: Derivative rule approach to Stieltjes and spectral imaging. Computing in Science and Engineering 23 (4), pp. 91.

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ISSN 1521-9615, Document, Link

Referenced by:

§18.39(iv), §18.40(ii).

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Relationships between the zeros, weights, and weight functions of orthogonal polynomials: Derivative rule approach to Stieltjes and spectral imaging. Computing in Science and Engineering 23 (3), pp. 56–64.

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ISSN 1521-9615, Document, Link

Referenced by:

§18.39(iv), §18.40(ii).

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8: Bibliography P

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Exactification of the method of steepest descents: The Bessel functions of large order and argument. Proc. Roy. Soc. London Ser. A 460, pp. 2737–2759.

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ISSN 1364-5021, Document, MathReview (F. Ursell), ZentralBlatt

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§10.20(ii).

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Automatic computation of Bessel function integrals. Comput. Phys. Comm. 25 (3), pp. 289–295.

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Notes:

Double-precision Fortran, maximum accuracy 20S.

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ISSN 0010-4655, Document, Code

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6th item.

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Modified Clenshaw-Curtis method for the computation of Bessel function integrals. BIT 23 (3), pp. 370–381.

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ISSN 0006-3835, Document, MathReview (H. E. Fettis), ZentralBlatt

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§10.74(vii).

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Fast analytic formulas for the modified Bessel functions of imaginary order for spectral line broadening calculations. J. Quantit. Spec. and Rad. Trans. 62 (4), pp. 389–395.

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External Links:

Document

Referenced by:

§10.76(ii).

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A method for computing Bessel function integrals. J. Comput. Phys. 75 (2), pp. 334–344.

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ISSN 0021-9991, Document, MathReview (J. G. Herriot), ZentralBlatt

Referenced by:

§10.74(vii), §10.74(vii).

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9: Bibliography S

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Spectral Methods in Chemistry and Physics. Applications to Kinetic Theory and Quantum Mechanics. Scientific Computation, Springer-Verlag, Dordrecht.

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External Links:

ISBN 978-94-017-9453-4; 978-94-017-9454-1, Document, Link, MathReview (Gabriel Stoltz)

Referenced by:

§18.38(i), §18.39(iii), §18.39(iii), §18.39(iii).

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Orthogonal Polynomials on the Unit Circle. Part 2: Spectral Theory. American Mathematical Society Colloquium Publications, Vol. 54, American Mathematical Society, Providence, RI.

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ISBN 0-8218-3675-7, MathReview (P. L. Duren), ZentralBlatt

Referenced by:

§18.33(i), §18.33(vi).

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Szegő’s Theorem and Its Descendants. Spectral Theory for $L^2$ Perturbations of Orthogonal Polynomials. M. B. Porter Lectures, Princeton University Press, Princeton, NJ.

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External Links:

ISBN 978-0-691-14704-8, MathReview (Harry Dym)

Referenced by:

§18.2(xi).

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Multiparameter spectral theory in Hilbert space. Research Notes in Mathematics, Vol. 22, Pitman (Advanced Publishing Program), Boston, Mass.-London.

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ISBN 0-8224-8414-5, MathReview (F. H. Szafraniec), ZentralBlatt

Referenced by:

Profile Brian D. Sleeman.

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Numerical Methods Based on Sinc and Analytic Functions. Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.

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Notes:

Sinc-Pack, a set of 480 Matlab programs with a 470-page tutorial, is available for purchase from SINC, LLC by contacting Frank Stenger.

External Links:

ISBN 0-387-94008-1, MathReview (B. Boyanov), ZentralBlatt

Referenced by:

§3.3(vi), §3.4(i), §3.5(i).

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10: Bibliography B

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Pionic atoms. Annual Review of Nuclear and Particle Science 20, pp. 467–508.

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External Links:

Document

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§33.22(iv).

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Coulomb functions (negative energies). Comput. Phys. Comm. 20 (3), pp. 447–458.

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Notes:

Double-precision Fortran code.

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Document, Code

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1st item, 4th item.

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Asymptotic methods in enumeration. SIAM Rev. 16 (4), pp. 485–515.

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Document, MathReview (Bernard Harris), ZentralBlatt

Referenced by:

Ch.2.

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A new asymptotic representation for $\zeta (\frac{1}{2}+it)$ and quantum spectral determinants. Proc. Roy. Soc. London Ser. A 437, pp. 151–173.

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ISSN 0962-8444, MathReview (Jack Quine), ZentralBlatt

Referenced by:

§25.9.

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Numerical Methods for Least Squares Problems. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.

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External Links:

ISBN 0-89871-360-9, MathReview (Hongyuan Zha), ZentralBlatt

Referenced by:

§3.11(v).

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